An estimate of the dipole moment of particle clusters

When a cluster of particles is immersed in a uniform electric field, the particles are coupled together due to the mutual interaction among them. This interaction causes the dipole moment of the cluster to be dependent upon the spatial arrangement and relative permittivity of the particles and upon the cluster size. In this work, we attempt to estimate the dipole moment of finite cubic arrays of particles, in terms of that of particle chains which has been known. We assume that a chain may be replaced by a single equivalent sphere with the same dipole moment. With replacing the chain by equivalent sphere, a cluster is simplified to a planar array, and this planar array is simplified to a chain, then the dipole moment is obtained. Numerical calculations are performed. It is found that our results are acceptable.